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Electromagnetic Induction

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Electrical transformers. Calculate the mutual inductance of two conducting coils ... Mutual Inductance: Transformers. The self-induced voltage in the primary is: ... – PowerPoint PPT presentation

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Title: Electromagnetic Induction


1
Electromagnetic Induction
  • Chapter 22

2
Expectations
  • After this chapter, students will
  • Calculate the EMF resulting from the motion of
    conductors in a magnetic field
  • Understand the concept of magnetic flux, and
    calculate the value of a magnetic flux
  • Understand and apply Faradays Law of
    electromagnetic induction
  • Understand and apply Lenzs Law

3
Expectations
  • After this chapter, students will
  • Apply Faradays and Lenzs Laws to some
    particular devices
  • Electric generators
  • Electrical transformers
  • Calculate the mutual inductance of two conducting
    coils
  • Calculate the self-inductance of a conducting
    coil

4
Motional EMF
  • A wire passes through a uniform magnetic field.
    The length of the wire, the magnetic field, and
    the velocity of the wire are all perpendicular to
    one another

5
Motional EMF
  • A positive charge in the wire experiences a
    magnetic force, directed upward

6
Motional EMF
  • A negative charge in the wire experiences the
    same magnetic force, but directed downward
  • These forces tend to separate the charges.

7
Motional EMF
  • The separation of the charges produces an
    electric field, E. It exerts an attractive force
    on the charges

E
8
Motional EMF
  • In the steady state (at equilibrium), the
    magnitudes of the magnetic force separating
    the charges and the Coulomb force attracting
    them are equal.

E
9
Motional EMF
  • Rewrite the electric field as a potential
    gradient
  • Substitute this result back into our earlier
    equation

E
10
Motional EMF
  • Substitute this result back into our earlier
    equation

E
11
Motional EMF
  • This is called motional EMF. It results from the
    constant velocity of the wire through the
    magnetic field, B.

E
12
Motional EMF
  • Now, our moving wire slides over two other wires,
    forming a circuit. A current will flow, and
    power is dissipated in the resistive load

13
Motional EMF
  • Where does this power come from?
  • Consider the magnetic
  • force acting on the
  • current in the sliding
  • wire

14
Motional EMF
  • Right-hand rule 1 shows that this force opposes
    the motion of the wire. To move the wire at
    constant velocity requires an equal and opposite
    force.
  • That force does work
  • The power

15
Motional EMF
  • The forces magnitude was calculated as
  • Substituting
  • which is the same as the
  • power dissipated electrically.

16
Motional EMF
  • Suppose that, instead of being perpendicular to
    the plane of the sliding-wire circuit, the
    magnetic field had made an angle f with the
    perpendicular to that plane.
  • The perpendicular
  • component of B B cos f

17
Motional EMF
  • The motional EMF
  • Rewrite the velocity
  • Substitute

18
Motional EMF
  • L Dx is simply the change in the loop area.

19
Motional EMF
  • Define a quantity F
  • Then
  • F is called magnetic
  • flux.
  • SI units Tm2 Wb (Weber)

20
Magnetic Flux
  • Wilhelm Eduard Weber
  • 1804 1891
  • German physicist and mathematician

21
Faradays Law
  • In our previous result, we said that the induced
    EMF was equal to the time rate of change of
    magnetic flux through a conducting loop. This,
    rewritten slightly, is called Faradays Law
  • Why the minus sign?

22
Faradays Law
  • Michael Faraday
  • 1791 1867
  • English physicist
  • and mathematician

23
Faradays Law
  • To make Faradays Law complete, consider adding N
    conducting loops (a coil)
  • What can change the magnetic flux?
  • B could change, in magnitude or direction
  • A could change
  • f could change (the coil could rotate)

24
Lenzs Law
  • Here is where we get the minus sign in Faradays
    Law
  • Lenzs Law says that the direction of the induced
    current is always such as to oppose the change in
    magnetic flux that produced it.
  • The minus sign in Faradays Law reminds us of
    that.

25
Lenzs Law
  • Heinrich Friedrich Emil Lenz
  • 1804 1865
  • Russian physicist

26
Lenzs Law
  • Lenzs Law says that the direction of the induced
    current is always such as to oppose the change in
    magnetic flux that produced it.
  • What does that mean?
  • How can an induced current oppose a change in
    magnetic flux?

27
Lenzs Law
  • How can an induced current oppose a change in
    magnetic flux?
  • A changing magnetic flux induces a current.
  • The induced current produces a magnetic field.
  • The direction of the induced current determines
    the direction of the magnetic field it produces.
  • The current will flow in the direction (remember
    right-hand rule 2) that produces a magnetic
    field that works against the original change in
    magnetic flux.

28
Faradays Law the Generator
  • A coil rotates with a constant angular speed in a
    magnetic field.
  • but f changes
  • with time

29
Faradays Law the Generator
  • So the flux also changes with time
  • Get the time rate of change (a calculus problem)
  • Substitute into Faradays Law

30
Faradays Law the Generator
  • The maximum voltage occurs when
  • What makes the voltage larger?
  • more turns in the coil
  • a larger coil area
  • a stronger magnetic field
  • a larger angular speed

31
Back EMF in Electric Motors
  • An electric motor also contains a coil rotating
    in a magnetic field.
  • In accordance with Lenzs Law, it generates a
    voltage, called the back EMF, that acts to oppose
    its motion.

32
Back EMF in Electric Motors
  • Apply Kirchhoffs loop rule

33
Mutual Inductance
  • A current in a coil produces a magnetic field.
  • If the current changes, the magnetic field
    changes.
  • Suppose another coil is nearby. Part of the
    magnetic field produced by the first coil
    occupies the inside of the second coil.

34
Mutual Inductance
  • Faradays Law says that the changing magnetic
    flux in the second coil produces a voltage in
    that coil.
  • The net flux in the
  • secondary

35
Mutual Inductance
  • Convert to an equation, using a constant of
    proportionality

36
Mutual Inductance
  • The constant of proportionality is called the
    mutual inductance

37
Mutual Inductance
  • Substitute this into Faradays Law
  • SI units of mutual inductance Vs / A henry (H)

38
Mutual Inductance
  • Joseph Henry
  • 1797 1878
  • American physicist

39
Self-Inductance
  • Changing current in a primary coil induces a
    voltage in a secondary coil.
  • Changing current in a coil also induces a voltage
    in that same coil.
  • This is called self-inductance.

40
Self-Inductance
  • The self-induced voltage is calculated from
    Faradays Law, just as we did the mutual
    inductance.
  • The result
  • The self-inductance, L, of a coil is also
    measured in henries. It is usually just called
    the inductance.

41
Mutual Inductance Transformers
  • A transformer is two coils wound around a common
    iron core.

42
Mutual Inductance Transformers
  • The self-induced voltage in the primary is
  • Through mutual induction, and EMF appears in the
    secondary
  • Their ratio

43
Mutual Inductance Transformers
  • This transformer equation is normally written
  • The principle of energy conservation requires
    that the power in both coils be equal (neglecting
    heating losses in the core).

44
Inductors and Stored Energy
  • When current flows in an inductor, work has been
    done to create the magnetic field in the coil.
    As long as the current flows, energy is stored in
    that field, according to

45
Inductors and Stored Energy
  • In general, a volume in which a magnetic field
    exists has an energy density (energy per unit
    volume) stored in the field
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